Modular building systems are of great interest in architecture and building technology, both on earth and in outer space. The advantages go beyond mere novelty of building form or space structure configurations. Besides the integration of geometry and structure, the economy due to few prefabricated elements, easy assembly due to repetitive erection and construction procedures are among the more attractive goals. Among the modular building systems, a system that permits both periodic and non-periodic configurations has the advantage of versatility over systems that do one or the other. In addition, the random-look of non-periodic configurations provide greater visual interest if carried out with an aesthetic sensitivity. Each designer, using a set of tiles from the present invention, could make up his or her own specific design different from others, each new and unique. This is an advantage absent in the periodic tiles and in rule-based non-periodic tiles. In addition, the tiles are fun to play with. Further, if the same pieces can be re-arranged in a variety of periodic as well as non-periodic ways, the designer is afforded a great flexibility in the design process.
In some cases, as in the case of masons who lay tiles in architectural environments, the freedom to design his or her own signature tiling pattern exists as a possibility. Another example would be astronauts assembling space structures in orbit. This advantage is inter-active, and designs can be modified as they are being realized. This is a possible advantage that can can be extended to robotic and computer-aided assembly of modular building systems.
This patent focusses mainly on various shapes of tiles and the tiling configurations generated by using these tiles. The tiles can be converted to upright or inclined prisms of any height. Such prisms provide alternative blocks and bricks for physical environments, architecture, art and sculptural objects, toys, games and puzzles. When only the outside surface planes of the prisms are used, and approporiately designed openings are made in these planes, usable and habitable architectural spaces can be defined.
The prior art in this field includes numerous U.S. patents. U.S. Pat. No. 1,474,779 to A. Z. Kammer discloses periodic tiling based on mirror-symmetric even-sided polygons derived from regular polygons. U.S. Pat. No. 4,133,152 to R. Penrose discloses a non-periodic tiling composed of two rhombic tiles based on the pentagon. U.S. Pat. No. 4,223,890 to A. Schoen discloses dissections of regular polygons into rhombii and singly-concave hexagons (i.e. a non-convex polygon with one concavity as described later in this application). U.S. Pat. No. 4,350,341 to Wallace discloses periodic and non-periodic patterns composed of odd-sided singly-concave polygons. U.S. Pat. No. 4,620,998 to H. Lalvani discloses periodic and non-periodic tilings composed of mirror-symmetric crescent-shaped tiles.
H. Lindgren's book `Recreational Problems in Geometric Dissections & How to Solve Them, (Dover, 1972), presents numerous examples of periodic tilings composed of convex and non-convex tiles obtained from dissections of regular polygons. The book, `Tilings and Patterns` by B. Grunbaum and G. Shephard, (W. H. Freeman, 1987), presents a large catalog of tilings. The relevant work in this book, in addition to Lindgren and Penrose (already cited), includes a non-periodic tiling based on Harborth's construction and composed of mirror-symmetric hexagons derived from a pentagon (p.52), Amman's non-periodic tiling composed of a square and a 45.degree. rhombus (p.556). In addition, D. R. Simonds (1977, 78) and G. Hatch (1978) in the journal Mathematics Teaching show examples of central and spiral tilings composed of "reflexed" 5-sided, 7-sided and 9-sided polygons. J. Baracs in Structural Topology journal (1979) discloses periodic tilings using convex zonogons.
Prior art, except for a few cases which are excluded in this application, does not teach periodic, non-periodic and central tilings based on `non-regular zonogons` and non-convex polygons derived from them, where all polygons are based on the concept of the central angles of regular p-sided polygonal nodes. Non-regular zonogons are even-sided convex polygons with a two-fold center of symmetry, and thus exclude the regular polygons which can be termed `regular zonogons`. The two-fold symmetry requires the edges (and angles) of non-regular zonogons to occur in pairs of opposite and parallel sides (and angles).